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A096579 Number of partitions of an n-set with exactly one even block. 9
0, 1, 3, 7, 25, 91, 329, 1415, 6297, 29431, 151085, 802099, 4506957, 26836083, 165586321, 1074740079, 7268876881, 50985776815, 372854157589, 2820244541675, 22087612114805, 179014336044171, 1495539626297689, 12894921568568999, 114481871464864825 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..591

FORMULA

E.g.f.: exp(sinh(x))*(cosh(x)-1). More generally, e.g.f. for the number of partitions of n-set with exactly k even blocks is 1/k!*exp(sinh(x))*(cosh(x)-1)^k.

MAPLE

b:= proc(n, t) option remember; `if`(n=0, t, add(

      `if`(t=1 and j::even, 0, binomial(n-1, j-1)*

       b(n-j, `if`(j::even, 1, t))), j=1..n))

    end:

a:= n-> b(n, 0):

seq(a(n), n=1..30);  # Alois P. Heinz, May 10 2016

MATHEMATICA

Drop[ Range[0, 24]! CoefficientList[ Series[ E^Sinh[x]*(Cosh[x] - 1), {x, 0, 24}], x], 1] (* Robert G. Wilson v, Aug 17 2004 *)

CROSSREFS

Cf. A003724.

Sequence in context: A129084 A287892 A002870 * A120540 A176829 A133206

Adjacent sequences:  A096576 A096577 A096578 * A096580 A096581 A096582

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 13 2004

EXTENSIONS

More terms from Robert G. Wilson v, Aug 17 2004

STATUS

approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)